A395167 Decimal expansion of the circumradius of a uniform 9-gonal antiprism with unit edges.

1, 5, 2, 4, 0, 4, 5, 5, 5, 1, 2, 6, 9, 8, 4, 2, 2, 6, 2, 9, 3, 0, 6, 6, 0, 5, 1, 4, 0, 1, 0, 7, 4, 5, 6, 2, 9, 4, 5, 5, 4, 3, 8, 3, 6, 4, 5, 6, 7, 6, 8, 0, 2, 8, 7, 4, 5, 0, 8, 1, 8, 8, 5, 6, 1, 0, 1, 9, 1, 7, 6, 2, 7, 2, 7, 7, 6, 6, 3, 6, 5, 7, 7, 1, 4, 6, 1, 6, 7, 0

Offset

1,2

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Polytope Wiki, Enneagonal antiprism.

Eric Weisstein's World of Mathematics, Antiprism.

Wikipedia, Antiprism.

Index entries for algebraic numbers, degree 6.

Formula

Equals sqrt(4 + csc(Pi/18)^2)/4.

Equals sqrt((3 - 2*cos(Pi/9))/(8 - 8*cos(Pi/9))) = sqrt((3 - 2*A019879)/(8 - 8*A019879)).

Equals the largest root of 64*x^6 - 192*x^4 + 108*x^2 - 17.

Example

1.52404555126984226293066051401074562945543836...

Mathematica

First[RealDigits[Sqrt[4 + Csc[Pi/18]^2]/4, 10, 100]]
(* Alternative: *)
First[RealDigits[PolyhedronData["NonagonalAntiprism", "Circumradius"], 10, 100]]

Crossrefs

Cf. A395164 (volume), A395165 (surface area), A395166 (midradius), A395168 (height).

Cf. A395169, A395170 (dihedral angles).

Cf. A019879.

Sequence in context: A214662 A277581 A307381 * A256167 A207528 A019901

Adjacent sequences: A395164 A395165 A395166 * A395168 A395169 A395170

Keyword

nonn,cons,easy

Author

Paolo Xausa, Apr 23 2026

Status

approved